How Do You Calculate Resonant Frequency and Irms in a Series RLC Circuit?

[cseet]

Hi all,

I've got this physics problem, I've tried solving it but do not know for sure the steps I took are correct. pls kindly advise and redirect me if I've got it wrong... thanks

A series RLC circuit with L=11mH, C=2.9uF, and R=4.3ohm is driven by a generator with a max emf of 155V and a variable frequency w (omega)

a) find the resonant frequency (units: rad/s)

answer:
R = V/I = 155/4.3 = 3.6A

XL = Vmax / Imax = 155/36 = 4.3

XL = wL
w = 4.3/11E-3 = 391rad/s

b) find Irms at resonance when w = 7.6E3 rad/s

XL = 7.6E3 * 11E-3
= 83.6 ohm
XL = V/I
I = V/XL
= 155/83.6
= 1.85A

pls direct me if I am wrong... appreciate it... I've learned more in this forum than in school...

thanks
cseet

 

[cseet]

Hi all,
I reckon b) 1.85A is the Imax therefore it should be 1.85 / square root of 2 = 1.31A?
pls advise
cseet

 

[Chen]

Resonant frequency is achieved when the reactances of the capacitor and induction coil are equal. The resistance of the resistor in this case doesn't matter, and neither do the maximum EMF or current.

X_L = X_C
\omega L = \frac{1}{\omega C}
\omega ^2 = \frac{1}{LC}

I get a value of 5.6E3 rad/s.

As for the second part, I don't quite understand why it says "find Irms at resonance when w = 7.6E3 rad/s", because, as I just demonstrated, the circuit is only at resonance for ω = 5.6E3 rad/s. But, I will show you how to find I(rms) regardless, since you went about it the wrong way (you found the current through the coil alone, not the circuit as a whole). The overall 'resistance' of the circuit is Z, which is:

Z^2 = R^2 + (X_L - X_C)^2

So the average current is:

I_{rms} = \frac{V_{rms}}{Z} = \frac{\frac{V_{max}}{\sqrt{2}}}{\sqrt{R^2 + (X_L - X_C)^2}}

Where XL and XC both depend on \omega;.